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INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY x (200x), #Axx REPRESENTATION NUMBERS OF STARS
 

Summary: INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY x (200x), #Axx
REPRESENTATION NUMBERS OF STARS
Reza Akhtar
Department of Mathematics, Miami University, Oxford, OH 45056, USA
reza@calico.mth.muohio.edu
Anthony B. Evans
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA
anthony.evans@wright.edu
Dan Pritikin
Department of Mathematics, Miami University, Oxford, OH 45056, USA
pritikd@muohio.edu
Received: , Revised: , Accepted: , Published:
Abstract
A graph G has a representation modulo r if there exists an injective map f : V (G)
{0, 1, . . . , r -1} such that vertices u and v are adjacent if and only if f(u)-f(v) is relatively
prime to r. The representation number rep(G) is the smallest positive integer r for which G
has a representation modulo r. In this paper we study representation numbers of the stars
K1,n. We will show that the problem of determining rep(K1,n) is equivalent to determining
the smallest even k for which (k) n: we will solve this problem for "small" n and
determine the possible forms of rep(K1,n) for sufficiently large n.

  

Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)

 

Collections: Mathematics